22P3Q03

3ai)

\displaystyle \begin{aligned}   \omega &=1200\times 2\pi \div 60 \\  &=126\text{ rad }{{\text{s}}^{-1}} \end{aligned}

3aii)

\displaystyle \begin{aligned}   ({{F}_{net}}&=ma) \\  F-mg&=mr{{\omega }^{2}} \\  F-(1.20)(9.81)&=(1.20)(0.230){{(126)}^{2}} \\  F&=4382+11.772 \\  &=4390\text{ N} \end{aligned}

COMMENT: Pls check that you included the weight of the towel in your calculation. Even though it is small compared to the centripetal force, you must include it in your working in order to score full marks.

3aiii)

4390 N at 1200 rpm is a very strong periodic driving force which can cause the washing machine to vibrate with large amplitude at \displaystyle 1200\div 60=20\text{ Hz}.

Large masses are placed at the base to lower the centre of gravity of the washing machine to prevent it from toppling.

Increasing the mass of the system also decreases the resonance frequency of the system, hopefully making it further away from the 20 Hz frequency of the driving force.

3b)

At the holes, the wall cannot exert any normal contact force on the water. So the water does not have the required centripetal force for circular motion.

The inertia and momentum of the water means that the water continues its motion in the tangential direction, thus leaving the drum through the holes.

COMMENT: Do not involve “centrifugal force” in your explanation because the “centrifugal force” is a fictitious force. (The rotating inertia frame is not in the H2 syllabus.) Explain using inertia and the absence of centripetal force instead.

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